Related papers: Normalizing Flow to Augmented Posterior: Condition…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…
Generative adversarial networks (GANs) and normalizing flows are both approaches to density estimation that use deep neural networks to transform samples from an uninformative prior distribution to an approximation of the data distribution.…
We tackle unsupervised anomaly detection (UAD), a problem of detecting data that significantly differ from normal data. UAD is typically solved by using density estimation. Recently, deep neural network (DNN)-based density estimators, such…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
This work investigates the nonparametric estimation of the vector field of a noisy Ordinary Differential Equation (ODE) in high-dimensional ambient spaces, under the assumption that the initial conditions are sampled from a…
Building on the recent trend of new deep generative models known as Normalizing Flows (NF), simulation-based inference (SBI) algorithms can now efficiently accommodate arbitrary complex and high-dimensional data distributions. The…
Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent…
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF).…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Neural Processes (NPs) are appealing due to their ability to perform fast adaptation based on a context set. This set is encoded by a latent variable, which is often assumed to follow a simple distribution. However, in real-word settings,…
Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise…
A flexible discriminative image denoiser is introduced in which multi-task learning methods are applied to a densoising FCN based on U-Net. The activations of the U-Net model are modified by affine transforms that are a learned function of…
While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…